An overlapping generations model is set up in this paper to analyze social security policy in a representative democracy with asymmetric information. The model considers not only redistribution between generations but also redistribution within generations according to individual labor incomes. Labor supply and savings are endogenous. The government is able to observe labor incomes, but not labor supply, savings or capital incomes. Two main results are derived in this setting: First, consumption levels are perfectly equalized within both generations. Second, a redistribution bias exists in favor of the old generation: the old generation receives a higher level of consumption than the young generation although both generations have the same weight in the objective function of the government.